PUBDET 2023 Question Paper Economis Statistics Maths

Paper - III
Subject : Mathematics & English
for admission in
Economics/Statistics/Mathematics
(Booklet Number)
Duration : 90 Minutes No. of Questions : 50 Full Marks : 100

INSTRUCTIONS
1. All questions are of objective type having four answer options for each. Only one option is
correct. Correct answer will carry full marks 2. In case of incorrect answer or any
combination of more than one answer, ½ mark will be deducted.
2. Questions must be answered on OMR sheet by darkening the appropriate bubble marked A,
B, C, or D.
3. Use only Black/Blue ink ball point pen to mark the answer by complete filling up of the
respective bubbles.
4. Mark the answers only in the space provided. Do not make any stray mark on the OMR.
5. Write question booklet number and your roll number carefully in the specified locations of
the OMR Sheet. Also fill appropriate bubbles.
6. Write your name (in block letter), name of the examination centre and put your signature (as
is appeared in Admit Card) in appropriate boxes in the OMR Sheet.
7. The OMR Sheet is liable to become invalid if there is any mistake in filling the correct
bubbles for question booklet number/roll number or if there is any discrepancy in the
name/signature of the candidate, name of the examination centre. The OMR Sheet may also
become invalid due to folding or putting stray marks on it or any damage to it. The
consequence of such invalidation due to incorrect marking or careless handling by the
candidate will be the sole responsibility of candidate.
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pen, log table, wristwatch, any communication device like mobile phones, bluetooth etc.
inside the examination hall. Any candidate found with such prohibited items will be
reported against and his/her candidature will be summarily cancelled.
9. Rough work must be done on the question booklet itself. Additional blank pages are given in
the question booklet for rough work.
10. Hand over the OMR Sheet to the invigilator before leaving the Examination Hall.
11. This booklet contains questions in both English and Bengali. Necessary care and precaution
were taken while framing the Bengali version. However, if any discrepancy(ies) is/are found
between the two versions, the information provided in the English version will stand and will
be treated as final.
12. Candidates are allowed to take the Question Booklet after Examination is over.

Signature of the Candidate : ______________________________
(as in Admit Card)

Signature of the Invigilator : ______________________________

Eco.+Stat.+Maths 

SPACE FOR ROUGH WORK / l¡g L¡­Sl SeÉ S¡uN¡

Eco.+Stat.+Maths 2 

MATHEMATICS

1. If log 3 5  a , log 3 2  b ,then log 3 300 equals to

k¢c log 3 5  a , log 3 2  b qu, a­h log 3 300 q­h

(A) 2(1 + a + b) (B) 1+a+b
(C) 2(1 + 2a + 2b) (D) 2(1 – 2a – 2b)

z i
2. Let z be a complex number such that is purely imaginary. Then maximum value of
z 1
z   2  2i  is

z i
j­e Ll, z Hl©f HL¢V S¢Vm l¡¢n ­k f¤­l¡f¤¢l L¡Òf¢eL q­h z ­p­r­œ z   2  2i  -Hl
z 1
p­hÑ¡µQ j¡e qm

(A) 2 2 (B) 2

3 1
(C) (D)
2 2

3. For real a, b, c the roots of the equation

 x  a  x  b    x  b  x  c    x  c  x  a   0 are
(A) negative (B) positive
(C) real (D) imaginary

h¡Ù¹h a, b, c -Hl SeÉ  x  a  x  b    x  b  x  c    x  c  x  a   0 pj£Ll­Zl h£S…¢m
q­h
(A) GZ¡aÈL (B) de¡aÈL
(C) h¡Ù¹h (D) L¡Òf¢eL

Eco.+Stat.+Maths 3 

4. The numbers of 30-digit sequences using only three digits 0, 1 and 2 having exactly ten 1’s
is

öd¤j¡œ ¢ae¢V Aˆ 0, 1, 2 à¡l¡ ¢œn pcpÉl Ae¤œ²j NWe Ll¡ q­h HC dl­Zl ¢heÉ¡­p ¢WL 10¢V 1
hÉhq¡l Ll¡ q­µR HC pwMÉ¡ qm

 A  30 P10 .210  B 30 C10 .220  C  30 C20 .210  D  30 C20

5. Consider the expression f  n   10n 1  10n  1 n  .

(A) ∄ any prime integer which divides f(n)

(B) ∃ a prime integer which divides f(n)

(C) f(n) is divisible by 5

(D) f(n) is divisible by 10

f  n   10n 1  10n  1 n  -HC l¡¢n¢V

(A) LMeC ­L¡e ­j±¢mL pwMÉ¡ à¡l¡ ¢hi¡SÉ eu f(n)

(B) Hje ­j±¢mL pwMÉ¡l A¢Ù¹aÆ l­u­R k¡l à¡l¡ ¢hi¡SÉ qu f(n)
(C) f(n), 5 à¡l¡ ¢hi¡SÉ

(D) f(n), 10 à¡l¡ ¢hi¡SÉ

6. Let P, Q be 3×3 matrices with P≠Q. If P3  Q3 and P 2Q  Q 2 P , then determinant value
of (P 2  Q 2 ) is equal to

j­e Ll, P J Q c¤¢V 3×3 j¡œ¡l jÉ¡¢VÊ„, P≠Q z k¢c P3  Q3 Hhw P 2Q  Q2 P qu, a­h (P 2  Q 2 ) -
Hl ¢eZÑ¡u­Ll j¡e q­h
(A) 1 (B) 0

(C) –1 (D) –2

Eco.+Stat.+Maths 4 

 2 0 5
 
7. Let A   1 2 3  . The system of linear equations AX=Y has a solution
 1 5 1 
 

x
 
(A) only for Y   0  , x 
0
 

0
 
(B) only for Y   y  , y 
0
 

0
 
(C) only for Y   y  , y, z 
z
 

(D) for all Y  3

 2 0 5
j­e Ll, A   1 2 3  °l¢ML pj£LlZ fËZ¡m£ AX=Y -Hl pj¡d¡e B­R
 1 5 1 
 

x
 
(A) öd¤j¡œ Y   0  , x  -Hl SeÉ
0
 

0
(B) öd¤j¡œ Y   y  , y  -Hl SeÉ
0
 

0
(C) öd¤j¡œ Y   y  , y, z  -Hl SeÉ
z
 

(D) pLm Y  3-Hl SeÉ

Eco.+Stat.+Maths 5 

2
8. If , , ,  are independent of x and in A.P. and  f (x)dx  4 , where
0

x  x  x 
f x  x   x x  1 then the common difference d is
x x x  
(A) only 1 (B) only –1
1
(C) ±1 (D) 
2
k¢c , , ,  ; x-Hl Efl ¢eiÑln£m e¡ qu Hhw A.P. ­a b¡­L Hhw
x  x  x  2
f x  x   x x 1 qu J  f (x)dx  4 qu a­h pj¡¿¹l fËN¢a¢Vl (A.P-Hl)
x x x   0

p¡d¡lZ A¿¹l d q­h
(A) öd¤j¡œ 1 (B) öd¤j¡œ –1
1
(C) ±1 (D) 
2

9. Let (a1, a2), (b1, b2) and (c1, c2) be three non collinear points in the xy-plane. Let r, s, t be
three real numbers such that (i) r+ s+ t=0, (ii) ra1+ sb1+ tc1=0, (iii) ra2+sb2+tc2=0. Then
(A) r=0, s=0, t=0 is the only solution.
(B) the system of equation may have finite number of non-trivial solutions.
(C) the given system is inconsistent.
(D) the system has infinitely many solutions.
j­e Ll, (a1, a2), (b1, b2), (c1, c2) -a­m ¢ae¢V fËcš ¢h¾c¤ , k¡l¡ pj­lM eu xy- pjam z r, s, t
¢ae¢V h¡Ù¹h pwMÉ¡ k¡l¡ (i) r+ s+ t=0, (ii) ra1+ sb1+ tc1=0 J (iii) ra2+sb2+tc2=0 pÇfLÑœu­L ¢pÜ
L­l z ­p­r­œ
(A) r=0, s=0, t=0 HLj¡œ pj¡d¡e

(B) pj£LlZ fËZ¡m£l pp£j pwMÉL An§eÉ pj¡d¡e B­R
(C) fËcš pj£LlZ fËZ¡m£ Ap‰a
(D) pj£LlZ fËZ¡m£l Ap£j pwMÉL An§eÉ pj¡d¡e B­R

Eco.+Stat.+Maths 6 

10. Let A= {x: x∈ , |x|<1} and B= {x: x∈ , |x-1|≥1} and A  B  – D.
D Then the set D is

j­e Ll, A= {x: x∈ , |x|<1} Hhw B= {x: x∈ , |x-1|≥1} Hhw A  B  – D z aMe D ­pV
q­h

(A) {x: x∈ ,1≤x≤2}

(B) {x: x∈ ,1≤x<2}

(C) {x: x∈ ,1<x≤2}

(D) {x: x∈ ,1<x<2}

A 1 B 1
11. For two events A and B, if P  A   P    and P    then
B 4 A 2
(A) A and B are independent

 A  3
(B) P  
B 5

 B  1
(C) P  
 A  3

A 2
(D) P  
 B  10

c¤¢V C­i¾V A J B Hl ­r­œ k¢c P  A   P    J P    qu a­h,
A 1 B 1
B 4 A 2

(A) A J B ¢eiÑln£m eu

 A  3
(B) P  
B 5

 B  1
(C) P  
 A  3

A 2
(D) P  
 B  10

Eco.+Stat.+Maths 7 

1 x2  1 x2
12. If tan 1   , then x2 is equal to
1 x  1 x
2 2

1 x2  1 x2
k¢c tan 1   qu, a­h x2-Hl j¡e q­h
1 x  1 x
2 2

(A) sin  (B) cos 

 (C) sin 2 (D) cos 2

 
13. The equation r 2 cos 2      3 represents
 6

(A) a parabola (B) a hyperbola

(C) a circle (D) a pair of straight lines

 
r 2 cos 2      3 pj£LlZ¢V
 6

(A) A¢dhªš (B) fl¡hªš
(C) hªš (D) plm­lM¡ k¤Nm p§¢Qa L­l

14. If x1, x2, x3 and y1, y2, y3 are both in G.P. with same common ratio, then the points (x 1, y1),
(x2, y2) and (x3, y3)

(A) are the vertices of a triangle (B) lie on a straight line

(C) lie on an ellipse (D) lie on a circle

x1, x2, x3 Hhw y1, y2, y3 HLC p¡d¡lZ Ae¤f¡apq …­Z¡šl fËN¢a­a B­R z ­p­r­œ (x1, y1), (x2,

y2) J (x3, y3) ¢h¾c¥œu

(A) HL¢V ¢œi¥­Sl ¢ae¢V ­L±¢ZL ¢h¾c¥ (B) ¢h¾c¥œu pj­lM¡¢ÙÛa
(C) ¢h¾c¥œu HL¢V Efhªš¢ÙÛa (D) ¢h¾c¥œu HL¢V hªš¢ÙÛa

Eco.+Stat.+Maths 8 

15. Let P, Q, R be three points on a parabola y 2  4ax , a  0 whose ordinates are in
geometrical progression. Then the tangents at P and R meet on

(A) the line through Q parallel to x-axis

(B) the line through Q parallel to y-axis

(C) the line joining Q to the vertex

(D) the line joining Q to the focus

A¢dhªš y 2  4ax , a  0 -H P, Q, R -Hje ¢ae¢V ¢h¾c¥ ­k a¡­cl ­L¡¢V…¢m …­Z¡šl fËN¢a­a B­R z
­p­r­œ P J R -H A¢dhª­š A¢ˆa ØfnÑLàu

(A) x-A­rl pj¡¿¹l¡m, Q ¢h¾c¥N¡j£ ­lM¡u ¢j¢ma qu

(B) y-A­rl pj¡¿¹l¡m, Q ¢h¾c¥N¡j£ ­lM¡u ¢j¢ma qu

(C) Q Hhw A¢dhª­šl n£oÑ¢h¾c¥l pwk¤š² plm­lM¡u ¢j¢ma qu

(D) Q Hhw A¢dhª­šl e¡¢il pwk¤š² ­lM¡u ¢j¢ma qu

x2 y
16. The normal at the end of the latus rectum to the ellipse   1 passes through an end
a 2 b2
of the minor axis if

x2 y
Efhªš   1 -Hl e¡¢im­ðl fË¡¿¹¢h¾c¥­a A¢ˆa A¢imð Efhªš¢Vl Ef¡­rl fË¡¿¹¢h¾c¥ ¢cu¡ k¡u z
a 2 b2
­p­r­œ

(A) e4 + e2 = 1

(B) e4 – e2 = 1

(C) e3 + e = 1

(D) e3 – e = 1

Eco.+Stat.+Maths 9 

x 2 y2 x2 y2
17. For the ellipses   1 and   1, t  \\{0}.
o Which of the following are
9 16 9  t 2 16  t 2
the same ?
(A) focus (B) latus rectum
(C) auxiliary circle (D) eccentricity

x 2 y2 x2 y2
Efhªšàu  1 J   1, t  \{0}
\ o-¢e­jl
À ­L¡e¢V/­L¡e…¢m HLC
9 16 9  t 2 16  t 2
fkÑ¡ui¥š² ?
(A) e¡¢i (B) e¡¢imð
(C) pq¡uLhªš (D) Ev­L¾cÊa¡

t
18. Two lines x = 1 + s, y = –3 –  s , z =1 +  s and x = , y = 1 + t, z = 2 –t, where s and t are
2
parameters, are perpendicular to each other, if  equals to

t
plm­lM¡àu x = 1 + s, y = –3 – s , z =1 + s Hhw x = , y = 1 + t, z = 2 –t, ­kM¡­e s J t
2
fË¡Qm, flØfl mð q­m  -Hl j¡e q­h
1
(A) 1 (B)
2

1
(C) 2 (D)
4

19. The intersection of the planes x  2y  3z  1  0 , x  y  z  1  0 and y  z  0 is

(A) a straight line (B) a void set

(C) a point (D) a plane

amœu x  2y  3z  1  0 , x  y  z  1  0 , y  z  0 - Hl ­Rc qm HL¢V

(A) plm­lM¡ (B) n§ZÉ­pV
(C) ¢h¾c¤ (D) am

Eco.+Stat.+Maths 10 

0, x  0
1
  x, 0  x  1
2 2
 1 1
20. Let f :  0,1  be defined by f  x    , x 
2 2
3 1
 2  x, 2  x  1

1, x  1

Then

(A) f is continuous in [0,1]

(B) f has removable discontinuity in [0,1] at three points

(C) f has jump discontinuity at only three points

(D) f is discontinuous everywhere

0, x  0
1
  x, 0  x  1
2 2
 1 1
j­e Ll, f :  0,1  Hi¡­h pw‘¡a ­k f  x    , x 
2 2
3 1
 2  x, 2  x  1

1, x  1

­p­r­œ

(A) f, [0,1]-H p¿¹a

(B) [0,1]-Hl ¢ae¢V ¢h¾c¥­a f -Hl Afp¡lZ­k¡NÉ Ap¿¹¢a B­R

(C) j¡œ ¢ae¢V ¢h¾c¥­a f-Hl EõÇge­k¡NÉ Ap¿¹¢a l­u­R

(D) f- A¿¹l¡­m phÑœC Ap¿¹a

Eco.+Stat.+Maths 11 

1, if x  1

21. Suppose f :  be given by f  x     x10 1 1
  x  1 sin
2
e , if x  1
x 1

then f  1

(A) does not exist (B) exists and is zero
(C) exists and is 9 (D) exists and is 10

1, if x  1

f:  Hi¡­h fËcš ­k f  x     x10 1 1 , k¢c x  1
  x  1 sin
2
e , if x  1
x 1

f  1 -Hl

(A) A¢Ù¹aÆ ­eC (B) A¢Ù¹aÆ B­R J j¡e n§eÉ
(C) A¢Ù¹aÆ B­R J j¡e 9 (D) A¢Ù¹aÆ B­R J j¡e 10

 2x  3  dy
22. If f   x   sin  log x  and y  f   then at x=1 is equal to
 3  2x  dx

2x  3 
k¢c f   x   sin  log x  qu J y  f 
dy
 qu, a­h x=1 ¢h¾c¤­a q­h
 3  2x  dx

(A) 6 sin log 5 (B) 5 sin log 6
(C) 12 sin log 5 (D) 5 sin log 12

23. Find which function does not obey Lagrange’s Mean value theorem in [0,1].

¢ejÀ A­frL…¢ml j­dÉ ­L¡e¢V Lagrange’l jdÉj¡e Eff¡cÉl naÑ¡hm£ f§lZ L­l e¡
1 1
 2  x, x  2  sin x
, x0

(A) f  x    2  B  f  x    x
 1  x  , x  1 1, x0
 2 
 2
C f  x   x x D f  x   x

Eco.+Stat.+Maths 12 

1
x sin x  1  cos x 
24. The least value of k for which lim 2  0 is
x 0 xk

1
x sin x  1  cos x 
k-Hl ­k r¥âaj j¡­el SeÉ lim 2  0 q­h ­p¢V qm
x 0 xk

(A) k = 1 (B) k=2 (C) k=3 (D) k = 4

 x 
25. lim   a  x  tan 
x a
 2a 

(A) does not exist (B) is 0

2a
(C) is (D) is e


 x 
lim   a  x  tan 
x a
 2a 

(A) -Hl A¢Ù¹aÆ ­eC (B) Hl j¡e 0
2a
(C) Hl j¡e (D) Hl j¡e e


26. Let I n   sec n xdx, n  . Then In is

j­e Ll, I n   sec n xdx, n  ,. aMe In q­h

sec n  2 x tan x n  2
A  I n  2 , for n  2
n 1 n 1
sec n 1 x tan 2 x n  1
 B  I n  2 , for n  2
n 1 n2
sec x tan n x n
C  cot x  In  2 , for n  2
n 1 n 1
cos ecn  2 x cot x n  1
 
D  I n  2 , for n  2
n 1 n2

Eco.+Stat.+Maths 13 

dx
27. Let I   . Then I=
13  3cos x  4sin x

dx
j­e Ll, I   , aMe I=
13  3cos x  4sin x

1 1 5 x 1 1  3 1 x
A tan 1   tan   c  B sin   cot   c
6 3 6 2 4 5 2 2
1 3 x 1 1 2 x
C cos 1   tan   c D tan 1   tan   c
3 4 4 4 4 5 2

(c: constant of integration)

(c: AhLme dËh
¤ L)

 n n n n 
28. lim       is
n  
 n 3
(n  4) 3
(n  8) 3
(n  4  n  1) 3



5 1 3 1
(A) (B)
2 5 2 3


(C) (D) 1
4

Eco.+Stat.+Maths 14 

29. If f  x   Pe2x  Qex  Rx, P, Q, R are constants, satisfies the condition f (0) = –1, and
log e 4
39
f   log e 2   31 and  f  x   Rx dx  2 , then
0

k¢c f  x   Pe2x  Qex  Rx, P, Q, R -dˤhL A­frL¢V f (0) = –1, Hhw f   loge 2   31
log e 4
39
J  f  x   Rx dx  , ­L ¢pÜ L­l, ­p­r­œ
0
2

(A) P = 5 (B) Q=6
(C) R=2 (D) P = 3

30. If a curve y = f(x) passes through a point (1, –1) and satisfies the differential equation
 1
y 1  xy  dx  xdy , then f    is equal to
 2
y = f(x) hœ²­lM¡¢V (1, –1) ¢h¾c¥N¡j£ Hhw y 1  xy  dx  xdy AhLm pj£LlZ­L ¢pÜ L­l z aMe
 1
f   =
 2
2 4
(A)  (B) 
5 5
2 4
(C) (D)
5 5
d2 y 2x dy y
31. Given    0 . By means of transformation x  tan  the given
dx 1  x dx 1  x 2 2
2 2

equation is changed to
d2 y 2x dy y
fËcš    0 , Qml¡¢n x  tan  f¢lhaÑ­el j¡dÉ­j fËcš pj£LlZ¢V ¢ejÀ
dx 1  x dx 1  x 2 2
2 2

BL¡­l l©f¡¿¹¢la qu
d2 y d2 y
A  2y  0  B  4y  0
d 2 d 2
d2 y d2y y
 C y0 D e  0
d 2 d 2

Eco.+Stat.+Maths 15 

x 2 1
If f  x    e  t dt , then the interval in which f(x) is increasing is
2
32.
x2

x 2 1
k¢c f  x    e  t dt qu a­h ­k A¿¹l¡­m f(x) A­frL œ²jhdÑj¡e q­h ­p¢V qm
2

x2

(A) (0, ) (B) (–, 0)
(C) [–2, 2] (D) [–1, 1]

1 1 1
33. Consider the curve 2
 2  2 where c is non-zero constant. If p be the length of the
x y c
perpendicular drawn from the origin to the tangent to the curve at a point corresponding to
parameter  then p2 =

1 1 1
hœ²­lM¡ 2
 2  2 , c An§eÉ dˤhL z hœ²­lM¡l Ef­l fË¡Qm  Hl Ae¤haÑ£ ­L¡e ¢h¾c¥­a A¢ˆa
x y c

ØfnÑ­Ll Efl j§m ¢h¾c¥ ­b­L A¢ˆa, mð°cOÑÉ p q­m p2 =

c2
A  B  c2
1  3sin 2  cos 2 
 C  c2 sin 2 cos 2  D  c2 sec  tan 

34. A spherical iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts
at a rate of 100 cm3/min. The rate at which the thickness of ice decreases where the
thickness of ice is 5 cm, is

10cm hÉ¡p¡­dÑl HL¢V ­N¡mL¡L«¢a ­m¡q¡l h­ml Efl pj¡e f¤l¦ hl­gl BÙ¹le ­cJu¡ B­R z k¢c
100 cm3/min q¡­l hlg Nm­a b¡­L a­h ­k q¡­l hl­gl ­hd Lj­h, kMe ­hd 5 cm a¡ qm

1 1
A cm / min  B cm / min
6 9
1 1
 C  cm / min  D  cm / min
25 3

Eco.+Stat.+Maths 16 

35. Consider the equation x 4  4x 3  2x 2  ax  b  0 where a, b are non-zero real numbers.
1
Given that for every root  of the equation, is also a root of the equation. Then

x  4x  2x  ax  b  0 pj£LlZ¢V (a J b An§ZÉ pwMÉ¡) ¢h­hQe¡ Ll z ­cJu¡ B­R ­k
4 3 2

1
pj£LlZ¢Vl fË¢a¢V h£S  -Hl ­r­œ -J pj£LlZ¢Vl HL¢V h£S q­h z ­p­r­œ

1
 A  a  1, b  1  B  a  2, b 
2
1
 C a  , b  3  D  a  4, b  1
3

36. A basic row operation on a matrix means adding a multiple of one row to another row.
 
 x 5 x   0 0 21 
   
Consider the matrices A   1 3 2  and B   1 1 14 
 2 2 2   4 
  0 4 
 3 
It is given that B can be obtained from A by applying finitely many basic row operations.
Then the value of x is

jÉ¡¢VÊ„ A-­a ‘h¤¢eu¡¢c p¡¢l Af¡­ln­el’ AbÑ jÉ¡¢VÊ„¢Vl ­L¡e p¡¢ll Ef¡c¡e…¢m­L ­L¡e pwMÉ¡ à¡l¡
x 5 x
…Z L­l ­pC …Zgm­L AeÉ p¡¢ll Ef¡c¡e pj§­ql p­‰ ­k¡N Ll¡ h¤T¡­h z A   1 3 2  ,
 2 2 2 
 
 
 0 0 21 
 
B   1 1 14  fËcš ­k B, A ­b­L pp£j pwMÉL p¡¢l Af¡­ln­el p¡q¡­kÉ f¡Ju¡ k¡u z
 4 
0 4 
 3 
­p­r­œ x q­h
(A) 3 (B) –3
(C) –1 (D) 2

Eco.+Stat.+Maths 17 

x
37. If y  (c: arbitrary non-zero constant) is the solution of the differential equation
log cx
y x x
y      ,  is differentiable function, then    is given by
x  y y
y x x
AhLm pj£LlZ y      -Hl (  -AhLm­k¡NÉ A­frL), HL¢V pj¡d¡e y  q­m
x  y log cx
x
(c kcªµR An§eÉ dˤhL)    q­h
y  
y2 y2 x2 x2
A  B  2 C (D) 
x2 x y2 y2

x 1
38. Let f (x)   x    x   x  , x 
2
1
(A) f(x) is continuous only at x 
2
1
(B) f(x) is discontinuous ∀ x 
2
1
(C) f(x) is continuous ∀ x 
2
1 
(D) f(x) is continuous only in  ,1
2 
x 1
j­e Ll, f (x)   x    x   x  , x 
2
1
(A) f(x) öd¤j¡œ x  ¢h¾c¥­a p¿¹a
2
1
(B) pLm x  Hl SeÉ f(x) Ap¿¹a q­h
2
1
(C) pLm x  Hl SeÉ f(x) p¿¹a q­h
2
1 
(D) öd¤j¡œ  ,1 -H f(x) p¿¹a q­h
2 

Eco.+Stat.+Maths 18 

39. The area of the portions cut off by the hyperbola x 2  3y 2  1 from the ellipse x 2  4y 2  8

is

Efhªš x 2  4y 2  8 ­b­L fl¡hªš x 2  3y 2  1 ­k Awn ­Rc L­l, a¡l ­rœgm q­h

 A  2 
2
3

log e 2  3   B    5 3 log e  2  5 
2
 C  2  log e 2  3
3
   D    5 3 log e  2  5 

40. The number of distinct real values of  for which the vectors  2 i  j  k , i   2 j  k and

i  j   2 k are coplanar, is

(A) zero (B) one

(C) two (D) three

 2 i  j  k , i   2 j  k J i  j   2 k HLam£u q­m  Hl h¡Ù¹h j¡­el pwMÉ¡ q­h

(A) n§eÉ (B) HL

(C) c¤C (D) ¢ae

Eco.+Stat.+Maths 19 

ENGLISH

41. Identify the pair of words that has the same relationship as the given pair :

democracy: elections

(A) carpenter: cistern

(B) gardener: earthworm

(C) gymnastics; pommel horse

(D) oceanography: aquifer

42. Given below is a Statement, followed by two Assumptions, (i) and (ii). Sometimes an
assumption is implicit in the statement. Read the sentences carefully and select the correct
option :

Statement : India is a member of SAARC, but she would do well to improve her ties
with ASEAN.

Assumption (i): India is planning to leave SAARC.

Assumption (ii): ASEAN is a stronger regional group than SAARC.

(A) (i) is correct but (ii) is incorrect.

(B) (i) is incorrect but (ii) is correct.

(C) Both (i) and (ii) are correct.

(D) Both (i) and (ii) are incorrect.

43. Select the word which is synonymous with - Interim.

(A) Interval

(B) Intermittent

(C) Timely

(D) Temporary

Eco.+Stat.+Maths 20 

44. Which disciplines are known as the ‘social sciences’?
(A) English, Bengali, Hindi
(B) History, Political Science, Anthropology
(C) Fine Arts, Martial Arts, Museology
(D) Law, Management Studies, Sports Management

45. Select the word that best replaces both the italicized phrases in the sentences given below:
Sentence (i) – The document was declared null and void.
Sentence (ii) – His claim was not justifiable.
(A) invalid
(B) adjustable
(C) immanent
(D) acrid

46. Choose the phrase that best replaces the italicized word in the given sentence :
Her arguments were trivial.
(A) difficult to understand
(B) totally garbled
(C) of little significance
(D) extremely relevant

47. Fill in the blanks in the given sentence with the most appropriate option :
Had the police not reached _____, the thieves ______.
(A) by time; will flee
(B) at time; will be fleeing
(C) this time; have fled
(D) in time; would have fled

Eco.+Stat.+Maths 21 

48. Identify, from the options given below, the sentence which has been correctly punctuated.

(A) To strive against all odds, in whatever situation of life you may be and to preserve
health --- health is wealth.

(B) To strive against all odds, in whatever situation of life you may be, and to preserve
health; health is wealth

(C) To strive against all odds in whatever situation of life you may be; and to preserve
health: health is wealth.

(D) To strive against all odds, in whatever situation of life you may be, and to preserve
health: health is wealth.

49. Fill the blanks with the appropriate words in the sets given below :

I could tell ____ the tone of his voice that he was really upset _____

me: ______ all probability, he felt somewhat responsible _______ my troubles.

(A) with, in, in, for

(B) for, by, with, in

(C) by, with, in, for

(D) in, for, by, with

50. Select the correct meaning for the idiomatic phrase – to sit on the fence.

(A) to prevent falling off

(B) to avoid taking sides

(C) to enjoy being outdoors

(D) to prove a point

_______________

Eco.+Stat.+Maths 22 

SPACE FOR ROUGH WORK / l¡g L¡­Sl SeÉ S¡uN¡

Eco.+Stat.+Maths 23 

Paper - III
Subject : Mathematics & English
for admission in
Economics/Statistics/Mathematics

pju: 90 ¢j¢eV ®j¡V fËnÀ : 50 ¢V f§ ZÑj¡e : 100

1. HC fËnÀf­œl ph fËnÀC Ah­S¢ƒi fËnÀ Hhw fË¢a¢V fË­nÀl Q¡l¢V pñ¡hÉ Ešl ­cJu¡ B­R
k¡l HL¢V j¡œ p¢WL z p¢WL Ešl ¢Q¢q²a Ll­m 2 eðl f¡­h z i¥m Ešl ¢Q¢q²a Ll­m
Abh¡ HL¡¢dL Ešl ¢Q¢q²a Ll­m ½ eðl L¡V¡ k¡­h z
2. OMR f­œ A, B, C, D ¢Q¢q²a p¢WL Ol¢V il¡V L­l Ešl ¢c­a q­h z
3. OMR f­œ Ešl ¢c­a öd¤j¡œ L¡­m¡ h¡ e£m L¡¢ml hm f­u¾V ­fe hÉhq¡l Ll­h z
4. OMR f­œ ¢e¢cÑø ÙÛ¡e R¡s¡ AeÉ ­L¡b¡J ­L¡­e¡ c¡N ­c­h e¡ z
5. OMR f­œ ¢e¢cÑø ÙÛ¡­e fËnÀf­œl eðl Hhw ¢e­Sl ­l¡m eðl A¢a p¡hd¡ea¡l p¡­b ¢mM­a
q­h Hhw fË­u¡Se£u Ol…¢m f§lZ Ll­a q­h z
6. OMR f­œ ¢e¢cÑø ÙÛ¡­e ¢e­Sl e¡j J fl£r¡­L­¾cÊl e¡j ¢mM­a q­h Hhw ¢e­Sl (Admit
Card H E­õ¢Ma) ü¡rl Ll­a q­h z
7. fËnÀf­œl eðl h¡ ­l¡m eðl i¥m ¢mM­m Abh¡ i¥m Ol il¡V Ll­m, fl£r¡bÑ£l e¡j,
fl£r¡­L­¾cÊl e¡j h¡ ü¡r­l ­L¡­e¡ i¥m b¡L­m Ešlfœ h¡¢am q­u ­k­a f¡­l z OMR
fœ¢V i¡yS q­m h¡ a¡­a Ae¡hnÉL c¡N fs­mJ h¡¢am q­u ­k­a f¡­l z fl£r¡bÑ£l HC
dl­el i¥m h¡ ApaÑLa¡l SeÉ Ešlfœ h¡¢am q­m HLj¡œ fl£r¡bÑ£ ¢e­SC a¡l SeÉ
c¡u£ b¡L­h z
8. ­j¡h¡Cm ­g¡e h¡ ®k ®L¡e dl®el C®mLVÌ¢eL NÉ¡®SV, LÉ¡mL¥­mVl, pÔ¡CXl¦m, mN­Vhm,
q¡aO¢s, ­lM¡¢Qœ, NË¡g h¡ ­L¡­e¡ dl­el a¡¢mL¡ , Lmj CaÉ¡¢c fl£r¡L­r Be¡ k¡­h e¡ z
Be­m ­p¢V h¡­Su¡ç q­h Hhw fl£r¡bÑ£l JC fl£r¡ h¡¢am Ll¡ q­h z
9. fËnÀf­œ l¡g L¡S Ll¡l SeÉ gy¡L¡ S¡uN¡ ­cJu¡ B­R z AeÉ ­L¡­e¡ L¡NS HC L¡­S
hÉhq¡l Ll­h e¡ z
10. fl£r¡Lr R¡s¡l B­N OMR fœ AhnÉC f¢lcnÑL­L ¢c­u k¡­h z
11. HC fËnÀf­œ Cwl¡S£ J h¡wm¡ Eiu i¡o¡­aC fËnÀ ­cJu¡ B­R z h¡wm¡ j¡dÉ­j fËnÀ °al£l
pju fË­u¡Se£u p¡hd¡ea¡ J paLÑa¡ Ahmðe Ll¡ q­u­R z a¡ p­šÄJ k¢c ­L¡e Ap‰¢a
mrÉ Ll¡ k¡u, ­p­r­œ Cwl¡S£ j¡dÉ­j ­cJu¡ fËnÀ ¢WL J Q¨s¡¿¹ h­m ¢h­h¢Qa q­h z
12. fl£r¡­n­o fl£r¡b£Ñl¡ fËnÀfœ¢V ¢e­u k¡­h z
Eco.+Stat.+Maths 24 
